Chapter 8: Planning Representing Actions State-space Representation Feature-based Representation STRIPS

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  • Representing Actions Planning

    Chapter 8:

    Planning

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 1

  • Representing Actions Planning

    Learning Objectives

    At the end of the class you should be able to:

    state the assumptions of deterministic planning

    represent a problem using both STRIPs and the feature-based representation of actions.

    specify the search tree for a forward planner

    specify the search tree for a regression planner

    represent a planning problem as a CSP

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 2

  • Representing Actions Planning

    Planning

    Planning is deciding what to do based on an agent’s ability, its goals, and the state of the world.

    Initial assumptions: I The world is deterministic. I There are no exogenous events outside of the control of

    the robot that change the state of the world. I The agent knows what state it is in. I Time progresses discretely from one state to the next. I Goals are predicates of states that need to be achieved

    or maintained.

    Aim find a sequence of actions to solve a goal.

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 3

  • Representing Actions Planning

    Classical Planning

    flat or modular or hierarchical

    explicit states or features or individuals and relations

    static or finite stage or indefinite stage or infinite stage

    fully observable or partially observable

    deterministic or stochastic dynamics

    goals or complex preferences

    single agent or multiple agents

    knowledge is given or knowledge is learned

    perfect rationality or bounded rationality

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 4

  • Representing Actions Planning

    State-space Representation Feature-based Representation STRIPS Representation

    Outline

    Representing Actions State-space Representation Feature-based Representation STRIPS Representation

    Planning Forward Planning Regression Planning Planning as a CSP

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 5

  • Representing Actions Planning

    State-space Representation Feature-based Representation STRIPS Representation

    Actions

    A deterministic action is a partial function from states to states.

    The preconditions of an action specify when the action can be carried out.

    The effect of an action specifies the resulting state.

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 6

  • Representing Actions Planning

    State-space Representation Feature-based Representation STRIPS Representation

    Delivery Robot Example

    Coffee Shop

    Mail Room Lab

    Sam's Office

    Features: RLoc – Rob’s location RHC – Rob has coffee SWC – Sam wants coffee MW – Mail is waiting RHM – Rob has mail

    Actions: mc – move clockwise mcc – move counterclockwise puc – pickup coffee dc – deliver coffee pum – pickup mail dm – deliver mail

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 7

  • Representing Actions Planning

    State-space Representation Feature-based Representation STRIPS Representation

    Explicit State-space Representation

    State Action Resulting State〈 lab, rhc , swc ,mw , rhm

    〉 mc

    〈 mr , rhc , swc ,mw , rhm

    〉〈 lab, rhc , swc ,mw , rhm

    〉 mcc

    〈 off , rhc , swc ,mw , rhm

    〉〈 off , rhc , swc ,mw , rhm

    〉 dm

    〈 off , rhc , swc ,mw , rhm

    〉〈 off , rhc , swc ,mw , rhm

    〉 mcc

    〈 cs, rhc , swc ,mw , rhm

    〉〈 off , rhc , swc ,mw , rhm

    〉 mc

    〈 lab, rhc , swc ,mw , rhm

    〉 . . . . . . . . .

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 8

  • Representing Actions Planning

    State-space Representation Feature-based Representation STRIPS Representation

    Feature-based representation of actions

    For each action:

    precondition is a proposition that specifies when the action can be carried out.

    For each feature:

    causal rules that specify when the feature gets a new value and

    frame rules that specify when the feature keeps its value.

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 9

  • Representing Actions Planning

    State-space Representation Feature-based Representation STRIPS Representation

    Example feature-based representation

    Precondition of pick-up coffee (puc):

    RLoc=cs ∧ rhc Rules for location is cs:

    RLoc ′=cs ← RLoc=off ∧ Act=mcc RLoc ′=cs ← RLoc=mr ∧ Act=mc RLoc ′=cs ← RLoc=cs ∧ Act 6= mcc ∧ Act 6= mc

    Rules for “robot has coffee”

    rhc ′ ← rhc ∧ Act 6= dc rhc ′ ← Act=puc

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 10

  • Representing Actions Planning

    State-space Representation Feature-based Representation STRIPS Representation

    STRIPS Representation

    Divide the features into:

    primitive features

    derived features. There are rules specifying how derived can be derived from primitive features.

    For each action:

    precondition that specifies when the action can be carried out.

    effect a set of assignments of values to primitive features that are made true by this action.

    STRIPS assumption: every primitive feature not mentioned in the effects is unaffected by the action.

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 11

  • Representing Actions Planning

    State-space Representation Feature-based Representation STRIPS Representation

    Example STRIPS representation

    Pick-up coffee (puc):

    precondition: [cs, rhc]

    effect: [rhc]

    Deliver coffee (dc):

    precondition: [off , rhc]

    effect: [rhc , swc]

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 12

  • Representing Actions Planning

    Forward Planning Regression Planning Planning as a CSP

    Outline

    Representing Actions State-space Representation Feature-based Representation STRIPS Representation

    Planning Forward Planning Regression Planning Planning as a CSP

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 13

  • Representing Actions Planning

    Forward Planning Regression Planning Planning as a CSP

    Planning

    Given:

    A description of the effects and preconditions of the actions

    A description of the initial state

    A goal to achieve

    find a sequence of actions that is possible and will result in a state satisfying the goal.

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 14

  • Representing Actions Planning

    Forward Planning Regression Planning Planning as a CSP

    Forward Planning

    Idea: search in the state-space graph.

    The nodes represent the states

    The arcs correspond to the actions: The arcs from a state s represent all of the actions that are legal in state s.

    A plan is a path from the state representing the initial state to a state that satisfies the goal.

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 15

  • Representing Actions Planning

    Forward Planning Regression Planning Planning as a CSP

    Example state-space graph

    mac

    Actions mc: move clockwise mac: move anticlockwise nm: no move puc: pick up coffee dc: deliver coffee pum: pick up mail dm: deliver mail

    mc

    mac

    mac

    mac

    mac

    mc

    mc mc

    puc

    〈cs,rhc,swc,mw,rhm〉

    〈cs,rhc,swc,mw,rhm〉 〈off,rhc,swc,mw,rhm〉 〈mr,rhc,swc,mw,rhm〉

    〈off,rhc,swc,mw,rhm〉

    〈mr,rhc,swc,mw,rhm〉

    〈lab,rhc,swc,mw,rhm〉 〈cs,rhc,swc,mw,rhm〉

    dc

    〈off,rhc,swc,mw,rhm〉

    〈lab,rhc,swc,mw,rhm〉

    〈mr,rhc,swc,mw,rhm〉

    Locations: cs: coffee shop off: office lab: laboratory mr: mail room

    Feature values rhc: robot has coffee swc: Sam wants coffee mw: mail waiting rhm: robot has mail

    c©D. Poole, A. Mackworth 2010, W. Menzel 2013 Artificial Intelligence, Lecture 8.1, Page 16

  • Representing Actions Planning

    Forward Planning Regression Planning Planning as a CSP

    What are the errors?

    puc

    Actions mc: move clockwise mac: move anticlockwise nm: no move puc: pick up coffee dc: deliver coffee pum: pick up mail dm: deliver mail

    mc

    mc

    mac

    puc

    puc

    mc

    mcmac

    pum

    〈mr,rhc,swc,mw,rhm〉

    〈mr,rhc,swc,mw,rhm〉 〈cs,rhc,swc,mw,rhm〉 〈mr,rhc,swc,mw,rhm〉

    〈lab,rhc,swc,mw,rhm〉

    〈cs,rhc,swc,mw,rhm〉

    〈off,rhc,swc,mw,rhm〉 〈cs,rhc,swc,mw,rhm〉

    〈mr,rhc,swc,mw,rhm〉

    〈off,rhc,swc,mw,rhm〉

    Locations:

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